Space/Time Hacks
Computer Output, Timing, and Usage
• 33345 min read
Over the course of my analysis on the Space Time Lecture I have learned many things, In these hacks I will cover; __.
Algorithm Complexity:
Algorithms that have a higher time complexity, such as those with nested loops or recursion, tend to take longer to execute compared to simpler algorithms. For example, an algorithm that has a time complexity of O(n^4) will take much longer to execute than an algorithm with a time complexity of O(n).
import time
def linear_search(arr, target):
start = time.time()
n = len(arr)
for i in range(n):
if arr[i] == target:
end = time.time()
print(f"Time taken: {end - start}")
return i
end = time.time()
print(f"Time taken: {end - start}")
return -1
arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
target = 7
index = linear_search(arr, target)
print(f"Target {target} found at index {index}")
Time taken: 2.86102294921875e-06 Target 7 found at index 6
import time
def slow_algorithm(n):
start = time.time()
result = 0
for i in range(n):
for j in range(n):
for k in range(n):
for l in range(n):
result += i + j * k - l
end = time.time()
print(f"Time taken: {end - start}")
return result
slow_algorithm(100)
Time taken: 16.931811809539795
245025000000
Input Data Size:
The time taken by an algorithm can also depend on the size of the input data. Algorithms that process larger amounts of data tend to take longer to execute than those that process smaller amounts of data. For example, a sorting algorithm that sorts a list of 10,000 items will take longer to execute than one that sorts a list of 10 items.
import random
import time
def sort_list(list_size):
# Generate a list of random integers with the specified size
my_list = [random.randint(1, 100) for _ in range(list_size)]
# Time how long it takes to sort the list
start_time = time.time()
sorted_list = sorted(my_list)
end_time = time.time()
# Print the sorted list and the time taken to sort it
print(f"Sorted list of size {list_size}: {sorted_list}")
print(f"Time taken to sort: {end_time - start_time} seconds")
sort_list(10) # Should be pretty fast
Sorted list of size 10: [10, 11, 12, 31, 32, 39, 56, 68, 93, 94] Time taken to sort: 5.0067901611328125e-06 seconds
sort_list(1000000) # Should take a bit longer
Sorted list of size 1000000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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sort_list(5000000) # Should take even longer
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